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Chapter 12 - Web Appendix 12C

# Chapter 12 - Web Appendix 12C - WEB APPENDIX 12C Using the...

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Unformatted text preview: WEB APPENDIX 12C Using the CAPM to Estimate the Risk-Adjusted Cost of Capital As an alternative to the subjective approach, firms can use the CAPM to directly estimate the cost of capital for specific projects or divisions. To begin, recall from Chapter 8 that the Security Market Line equation expresses the risk/return relationship: r s ¼ r RF þ ð RP M Þ b i As an example, consider the case of Erie Steel Company, an integrated steel producer operating in the Great Lakes region. For simplicity, assume that Erie uses only equity capital; so its cost of equity also is its corporate cost of capital, or WACC. Erie ’ s beta ¼ b ¼ 1.1, r RF ¼ 8%, and RP M ¼ 4%. Thus, Erie ’ s cost of equity and hence its WACC is 12.4%: r s ¼ WACC ¼ 8% þ ð 4% Þ 1 : 1 ¼ 12 : 4% This suggests that investors should be willing to give Erie money to invest in average-risk projects if the company expects to earn 12.4% or more on this money. Here again, by average risk, we mean projects having risk similar to the firm ’ s existing assets. Therefore, as a first approximation, Erie should invest in capital projects if and only if those projects have an expected return of 12.4% or more. 1 Erie should use 12.4% as its hurdle rate for an average-risk project. Suppose, however, that taking on a particular project would cause a change in Erie ’ s beta coefficient, which, in turn, would change the company ’ s cost of equity. For example, assume that Erie is considering the construction of a fleet of barges to haul iron ore and that barge operations have betas of 1.5 rather than 1.1. Since the firm itself may be regarded as a “ portfolio of assets ” and since the beta of any portfolio is a weighted average of the betas of its individual assets, taking on the barge project would cause the overall corporate beta to rise to somewhere between the original beta of 1.1 and the barge project ’ s beta of 1.5. The exact value of the new beta would depend on the relative size of the investment in barge operations versus Erie ’ s other assets. If 80% of Erie ’ s total funds ended up in basic steel operations with a beta of 1.1 and 20% ended up in barge operations with a beta of 1.5, the new corporate beta would be 1.18: New beta ¼ : 8 ð 1 : 1 Þ þ : 2 ð 1 : 5 Þ ¼ 1 : 18 This increase in Erie ’ s beta coefficient would cause its stock price to decline unless the increased beta was offset by a higher expected rate of return...
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Chapter 12 - Web Appendix 12C - WEB APPENDIX 12C Using the...

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